Improving neural networks by preventing co-adaptation of feature detectors
(2012)

When a large feedforward neural network is trained on a small training set, it typically performs poorly on held-out test data. This overfitting is greatly reduced by randomly omitting half of the feature detectors on each training case. This prevents complex co-adaptations in which a feature detector is only helpful in the context of several other specific feature detectors. Instead, each neuron learns to detect a feature that is generally helpful for producing the correct answer given the combinatorially large variety of internal contexts in which it must operate. Random “dropout” gives big improvements on many benchmark tasks and sets new records for speech and object recognition. A feedforward, artificial neural network uses layers of non-linear hidden units between its inputs and its outputs. By adapting the weights on the incoming connections of these hidden units it learns feature detectors that enable it to predict the correct output when given an input vector [15]. If the relationship between the input and the correct output is complicated and the network has enough hidden units to model it accurately, there will typically be many different settings of the weights that can model the training set almost perfectly, especially if there is only a limited amount of labeled training data. Each of these weight vectors will make different predictions on held-out test data and almost all of them will do worse on the test data than on the training data because the feature detectors have been tuned to work well together on the training data but not on the test data. Overfitting can be reduced by using “dropout” to prevent complex co-adaptations on the training data. On each presentation of each training case, each hidden unit is randomly omitted from the network with a probability of 0.5, so a hidden unit cannot rely on other hidden units being present. Another way to view the dropout procedure is as a very efficient way of performing model averaging with neural networks. A good way to reduce the error on the test set is to average the predictions produced by a very large number of different networks. The standard way to do this is to train many separate networks and then to apply each of these networks to the test data, but this is computationally expensive during both training and testing. Random dropout makes it possible to train a huge number of different networks in a reasonable time. There is almost certainly a different network for each presentation of each training case but all of these networks share the same weights for the hidden units that are present. We use the standard, stochastic gradient descent procedure for training the dropout neural networks on mini-batches of training cases, but we modify the penalty term that is normally used to prevent the weights from growing too large. Instead of penalizing the squared length (L2 norm) of the whole weight vector, we set an upper bound on the L2 norm of the incoming weight vector for each individual hidden unit. If a weight-update violates this constraint, we renormalize the weights of the hidden unit by division. Using a constraint rather than a penalty prevents weights from growing very large no matter how large the proposed weight-update is. This makes it possible to start with a